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MatPlus.Net Forum General Dombrovskis paradox
 
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(1) Posted by Oliver Petrov [Friday, Sep 24, 2010 19:41]; edited by Oliver Petrov [10-09-27]

Dombrovskis paradox


What is "Dombrovskis paradox" compared to just "Dombrovskis". They are different: look here: http://winchloe.free.fr/themes.html
 
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(2) Posted by seetharaman kalyan [Saturday, Sep 25, 2010 08:31]

The original Dobrovskis theme required two black defences, while the paradox can be demonstrated with only one black defence.
 
 
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(3) Posted by Paz Einat [Saturday, Sep 25, 2010 12:08]; edited by Paz Einat [10-09-25]

The Dombrovskis theme requires a refutation. However, in essence, the effect can be achieved with a regular defense.
This can be viewed as:
1.X? threat 2.A # but 1...a !
Solution:
1.Y !
1...a 2. A #
This is Dombrovskis (and needs to be doubled)

The Dombrovskis effect (Paradox) is:
1.X? threat 2.A #
1...a 2.B #
but 1...z !
Solution:
1.Y !
1...a 2. A #

What we see is that the defense 1...a defends against the threat in the try but there is a mate on this.
This mate is changed to the try threat in the solution.
So if the black defense has no mate on it (refutation) - this is Dombrovskis
If there is a mate on this defense (and there is another refutation) - this is Dombrovskis effect
 
   
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(4) Posted by Oliver Petrov [Saturday, Sep 25, 2010 12:20]

Thank you for the competent answer. My doubt is whether this is Dombrovskis:
1.X? threat 2.A# but 1....a!
1.Y? Threat 2.A# or B# but AGAIN 1...a!(THE SAME REFUTATION TO DIFFERENT TRY MOVES!!!)
Solution: 1.Z!
1..a 2.A#
 
   
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(5) Posted by Paz Einat [Saturday, Sep 25, 2010 13:53]

You have a Dombrovskis between the X try and the solution, even if there is only one try. The Y try does not add much,so it seems. If you have a threat B you need to have some play around it as well.

Regarding the same refutation to a different try move, indeed you added a "B" threat but often this can be trivial.
 
   
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(6) Posted by Oliver Petrov [Saturday, Sep 25, 2010 14:11]

Are you completely sure? I did read here that the pattern has to happen at least two times:
http://chess-problems-gr.blogspot.com/2008/09/dombrovskis-2-task_22.html
 
   
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(7) Posted by Paz Einat [Saturday, Sep 25, 2010 18:44]

Twice (at least) is the convention. However, since the essential pattern can be shown in one try/sol it can be regarded as Dombrovskis, though for a problem to be considered as showing the full theme twice is the minimum.
Obviously, showing only once can be rather dull and often many additional elements/themes are added.
 
   
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(8) Posted by Oliver Petrov [Saturday, Sep 25, 2010 20:00]

Thanks!
 
   
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(9) Posted by Jacques Rotenberg [Monday, Sep 27, 2010 00:56]

The Dombrovskis theme is not mainly a pattern theme, but a paradox.
I can be described as follow :

A black move "1...a", and a white move "A" are bound, in two plays, in opposite ways :

in one play "1...a" provokes "A"
in one play "1...a" forbids "A"

Alfreds Dombrovskis shew that as follow :

In a play : "A" is a threat, "1...a" is the refutation
you can write it 1.X? [A#] but 1...a!
In the solution "1...a" is a variation, and is followed with "2.A#"
this has to be shown at least twice, as follow :
1.X? [A#] but 1...a!
1.Y? [B#] but 1...b!
1.Z? [C#](or block)
1...a 2.A#
1...b 2.B#

This very precise scheme is the so called Dombrovskis theme.

But this paradoxical relationship between "1...a" and "A#" may be shown in many other ways
for example :
- "1...a" may be a defense against [A#] and not a refutation
- you may have double threats
- you may have the 2 variations needed by the theme but shown in different phases
- the LeGrand theme (1.X{2.A#] a 2.B# and 1.Y[B#] a 2.A#) may be seen as a reciprocal Dombrovskis paradox
... and many other ways that cannot be called "Dombrovskis theme" because it does not follow the full way described above.

For information - and pleasure - here is the first "Dombrovskis theme" :

Alfreds Dombrovskis
Probleemblad 1958
1st Prize
(= 7+8 )
2#

1.Bc1? [2.Sf4‡ A]
but 1…Bd2! a

1.Sg3? [2.Rd4‡ B]
but 1…Qe2! b

1.Se3!! [2.Qc2‡]
1…Bd2 a 2.Sf4‡ A
1…Qe2 b 2.Rd4‡ B
1…Ke2 2.Qd1‡
 
   
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(10) Posted by seetharaman kalyan [Monday, Sep 27, 2010 08:19]

The first example is still the best.
 
   
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(11) Posted by Jacques Rotenberg [Monday, Sep 27, 2010 12:23]

I don't know if the best, but in anycase, a great one !
When A. Dombrovskis defined his theme he also demanded that the changes will be done mainly by the key, and not by the keys of the tries !
 
 
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(12) Posted by Paz Einat [Monday, Sep 27, 2010 15:39]

By the way, there are over 20 problems showing the pattern which were published before the Dombrovskis problem, but this doesn't take any credit from Alfred Dombrovskis who clearly showed the paradox and composed a superb problem. The same s true for the Rukhlis theme.

Just as an example here's one problem:

A.W.L.Everts
Good Companion 1921
(= 7+2 )

#2
1.Qh2? 2.Sc8 A # but 1...Kxb6 a !
1.Qb2? 2.Sxc6 B # but 1...Kb8 b !
1.Qf7! zz
1...Kxb6 a 2.Sc8 A #
1...Kb8 b 2.Sxc6 B #
1...S~ 2.b8=Q #
 
 
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(13) Posted by Juraj Lörinc [Monday, Sep 27, 2010 16:10]

Actually, for me both qualifications in "The first example is still the best." seem to be wrong. Dombrovskis problem was not the first as already stated - and although good, it is far from the best in my view.

The key is excellent, but the motivation of moves is too heterogenous:
- 1.Bc1 anticritical move, 1...Bd2! proving also critical character
- 1.Sg3 guard of e2, 1...Qe2! pin of rook
- 1...Bd2 defends by cutting c2-e2
- 1...Qe2 directly guards c2

This is well known - and does not diminish by any means the novelty of the paradox as a key thematical element of a composition in 1950s.
 
   
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(14) Posted by Jacques Rotenberg [Monday, Sep 27, 2010 16:50]; edited by Jacques Rotenberg [10-09-27]

@ Juraj :

I don't fully agree, here due to the fact that every effect is different, you can feel that it is homogeneous and rich.
In fact, I specially like this variety of effects.

@ Paz :

Do you have in your collection of previous D. Th. something more interesting ? That one, as a D. Th., is not a big success!
 
   
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(15) Posted by Paz Einat [Monday, Sep 27, 2010 18:27]; edited by Paz Einat [10-09-27]

Most of the early problems are probably accidental and thus not as interesting as the later ones. Still, here are some examples:

Alfred Pries
1st Com Die Schwalbe 1951
(= 9+9 )

#2
1.Re4? 2.Sb4 A# 1...c2 a!
1.Re8? 2.Be4 B# 1...Be6 b!
1.Re3! zz
1...c2 a 2.Sb4 A#
1...Be6 b 2.Be4 B#

Rafael Candela Sanz
6th Com Die Schwalbe 1954
(= 11+7 )

#2
set
1...cxd1=~ x 2.Qxc6 A#
1...exd1=~ y 2.Qxe6 B#
1.b8=S? 2.Qxc6 A# 1...e5 a!
1.f8=S? 2.Qxe6 B# 1...c5 b!
1.Sd4! zz
1...e5 a 2.Qxc6 A#
1...c5 b 2.Qxe6 B#
Importantly:
1...cxd1=~ x 2.Qxe6 B#
1...exd1=~ y 2.Qxc6 A#
Reciprocal changes
 
   
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(16) Posted by Juraj Lörinc [Tuesday, Sep 28, 2010 08:33]

In the Pries problem, is there a missing bishop on g8? I am not sure, but it seems so.
 
   
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(17) Posted by Jacques Rotenberg [Tuesday, Sep 28, 2010 09:00]

it seems that the correct diagram is as follow :

(= 10+10 )

 
   
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(18) Posted by Paz Einat [Tuesday, Sep 28, 2010 14:35]

Indeed, I accidentally omitted the BBg8.
 
   
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(19) Posted by Jacques Rotenberg [Tuesday, Sep 28, 2010 18:38]; edited by Jacques Rotenberg [10-09-28]

not only .... But, it happens ...
 
   
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(20) Posted by Marjan Kovačević [Wednesday, Sep 29, 2010 02:37]

No one mentioned one more theme in the prototype by Mr. Dombrovskis, a theme that really makes this Dombrovskis example so memorable. I deeply believe Alfreds worked on that other theme, and was lucky to find the suitable relation between tries and refutations, as almost ready from the matrix itself. Later on, the more substantial theme became invisible and forgotten. Something similar happened to the excellent problems by Umnov, Hannelius and Salazar, responsible for the names of these themes.
What is the other theme in this famous problem by Dombrovskis?
 
   
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MatPlus.Net Forum General Dombrovskis paradox